Violations of CPT symmetry and Lorentz invariance are searched for by studying interference effects in B0 mixing and in Bs0 mixing. Samples of B0→J/ψKS0 and Bs0→J/ψK+K- decays are recorded by the LHCb detector in proton-proton collisions at center-of-mass energies of 7 and 8 TeV, corresponding to an integrated luminosity of 3 fb-1. No periodic variations of the particle-antiparticle mass differences are found, consistent with Lorentz invariance and CPT symmetry. Results are expressed in terms of the standard model extension parameter Δaμ with precisions of O(10-15) and O(10-14) GeV for the B0 and Bs0 systems, respectively. With no assumption on Lorentz (non)invariance, the CPT-violating parameter z in the Bs0 system is measured for the first time and found to be Re(z)=-0.022±0.033±0.005 and Im(z)=0.004±0.011±0.002, where the first uncertainties are statistical and the second systematic.